Development and Assessment of a Reconstructed Discontinuous Galerkin Method for the Compressible Turbulent Flows on Hybrid Grids

摘要

A third-order reconstructed discontinuous Galerkin (rDG(P_1P_2)) method is presented to solve the Reynolds-averaged Navier-Stokes (RANS) equations, along with the modified one-equation model of Spalart and Allmaras (SA) on 3D hybrid curved grids based on a coupled approach. In this method, a piecewise quadratic polynomial solution is obtained from the underlying piecewise linear DG solution using a hierarchical Weighted Essentially Non-Oscillatory (WENO) reconstruction. The reconstructed quadratic polynomial solution is then used for computing the inviscid and the viscous fluxes. The modified SA model is, however, discretized using the underlying second-order DG(P_1) method. A number of test cases are presented to assess the performance of the rDG(P_1P_2) method for turbulent flow problems. The numerical results demonstrate that the rDG(P_1P_2) method is able to achieve the designed third-order of accuracy at a cost slightly higher than its underlying second-order DG method, outperform the standard third order DG method in terms of both computing costs and storage requirements, and obtain reliable and accurate solutions to 3D compressible turbulent flows.